• Research in Mathematical Education
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• v.26 no.3
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• pp.147-166
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• 2023

Mathematics is a science of pattern. Mathematics is a subject of inquiring which aims at discovering the models hidden behind the world. Pattern is abstraction and generalization of the model. Mathematical pattern is a higher level of mathematical model. Mathematics patterns are often hidden in pattern similarity. Creation of mathematics lies largely in discovering the pattern similarity among the various components of mathematics. Inquiring is the core and soul of mathematics teaching. It is very important for students to study mathematics like mathematicians' exploring and discovering mathematics based on pattern similarity. The author describes an example about how to guide students to carry out mathematics inquiring based on pattern similarity in classroom.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.383-389
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• 2010

In this paper, we investigate h-stability of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.8
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• pp.2895-2912
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• 2014

Content-based image retrieval has been the most important technique for managing huge amount of images. The fundamental yet highly challenging problem in this field is how to measure the content-level similarity based on the low-level image features. The primary difficulties lie in the great variance within images, e.g. background, illumination, viewpoint and pose. Intuitively, an ideal similarity measure should be able to adapt the data distribution, discover and highlight the content-level information, and be robust to those variances. Motivated by these observations, we in this paper propose a probabilistic similarity learning approach. We first model the distribution of low-level image features and derive the free energy kernel (FEK), i.e., similarity measure, based on the distribution. Then, we propose a learning approach for the derived kernel, under the criterion that the kernel outputs high similarity for those images sharing the same class labels and output low similarity for those without the same label. The advantages of the proposed approach, in comparison with previous approaches, are threefold. (1) With the ability inherited from probabilistic models, the similarity measure can well adapt to data distribution. (2) Benefitting from the content-level hidden variables within the probabilistic models, the similarity measure is able to capture content-level cues. (3) It fully exploits class label in the supervised learning procedure. The proposed approach is extensively evaluated on two well-known databases. It achieves highly competitive performance on most experiments, which validates its advantages.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.393-407
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• 2009

In this article the definition of similarity and its introduction in Korean middle school textbooks based on the 7th national curriculum are analysed critically. As a result four suggestions are presented. First, on the consideration that the contents related with similarity has been removed in the elementary school curriculum, the meaning of 'constant rate' needs to be understood through the rich experience of drawing enlarged/reduced figures when similarity is introduced in middle school, Second, there are two different ways in enlargement/reduction of figures and in the definition of similarity. Teachers have to keep the limitations of the two ways in mind. Third, the activity of drawing similar figures in enlarged/reduced squared paper needs to be practiced. Last, on 'the relation of similarity' which is in the definition of similarity, it has to be examined whether 'similarity' should be presented in the documents of the national curriculum as a term.

• The Journal of the Korea Contents Association
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• v.12 no.3
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• pp.34-43
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• 2012

Determining the similarity between two strings can be applied various area such as information retrieval, spell checker and spam filtering. Similarity calculation between Korean strings based on dynamic programming methods firstly requires a definition of the similarity between phonemes. However, existing methods have a limitation that they use manually set similarity scores. In this paper, we propose a method to automatically calculate inter-phoneme similarity from a given set of variant words using a PAM-like probabilistic model. Our proposed method first finds the pairs of similar words from a given word set, and derives derivation rules from text alignment results among the similar word pairs. Then, similarity scores are calculated from the frequencies of variations between different phonemes. As an experimental result, we show an improvement of 10.1%~14.1% and 8.1%~11.8% in terms of sensitivity compared with the simple match-mismatch scoring scheme and the manually set inter-phoneme similarity scheme, respectively, with a specificity of 77.2%~80.4%.

• Language and Information
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• v.14 no.1
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• pp.113-144
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• 2010

The primary goal of this paper is to find a feasible way to answer the question: Does the similarity in meaning between verbs relate to the similarity in their subcategorization? In order to answer this question in a rather concrete way on the basis of a large set of English verbs, this study made use of various language resources, tools, and statistical methodologies. We first compiled a list of 678 verbs that were selected from the most and second most frequent word lists from the Colins Cobuild English Dictionary, which also appeared in WordNet 3.0. We calculated similarity measures between all the pairs of the words based on the 'jcn' algorithm (Jiang and Conrath, 1997) implemented in the WordNet::Similarity module (Pedersen, Patwardhan, and Michelizzi, 2004). The clustering process followed, first building similarity matrices out of the similarity measure values, next drawing dendrograms on the basis of the matricies, then finally getting 177 meaningful clusters (covering 437 verbs) that passed a certain level set by z-score. The subcategorization frames and their frequency values were taken from the ICE-GB. In order to calculate the Selectional Preference Strength (SPS) of the relationship between a verb and its subcategorizations, we relied on the Kullback-Leibler Divergence model (Resnik, 1996). The SPS values of the verbs in the same cluster were compared with each other, which served to give the statistical values that indicate how much the SPS values overlap between the subcategorization frames of the verbs. Our final analysis shows that the degree of overlap, or the relationship between semantic similarity and the subcategorization frames of the verbs in English, is equally spread out from the 'very strongly related' to the 'very weakly related'. Some semantically similar verbs share a lot in terms of their subcategorization frames, and some others indicate an average degree of strength in the relationship, while the others, though still semantically similar, tend to share little in their subcategorization frames.

• Journal of Korea Water Resources Association
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• v.31 no.5
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• pp.575-586
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• 1998

A relaxed similarity theory which can be applied to river models with movable beds is established by modifying existing theory by Einstein and chien(1954). Experimental data collected from river models with movable beds were used to evaluate the applicability of the proposed theory. Effects of similarity of flow, ΔFΔM, and similarity of sediment movement, ΔFs, were examined by analyzing the behaviour of total river-bed change. The results show that the smaller ΔFΔM or ΔFs is, respectively, the larger total sedimentation is. The modified similarity theory established in this study would be useful and practical whenever it is impossible or very difficult to satisfy strict theoretical requirements concerning the river model experiments with movable beds. Keywords : river model, similarity of flow, similarity of sediment movement, sediment transport, river-bed change.

• The Journal of the Korea institute of electronic communication sciences
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• v.19 no.1
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• pp.295-300
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• 2024

This paper discusses the incompleteness of the SNOMED CT and proposes a noble metric which evaluates similarity among sibling nodes as a method to address this incompleteness. SNOMED CT encompasses an extensive range of medical terms, but it faces issues of ontology incompleteness, such as missing concepts in the hierarchy. We propose a noble metric for evaluating similarity among nodes within a node group, composed of multiple sibling nodes, to identify missing concepts, and identify groups with low similarity. Analyzing the similarity of sibling node groups in the March 2023 international release of SNOMED CT, the average similarity of 29,199 sibling node groups, which are sub-concepts of the clinical finding concept and are consist of two or more sibling nodes, was found to be 0.81. The group with the lowest similarity was associated with child concepts of poisoning, with a similarity of 0.0036.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.11
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• pp.2824-2838
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• 2013

There has been a lot of attention paid recently to analyze dynamic human gestures that vary over time. Most attention to dynamic gestures concerns with spatio-temporal features, as compared to analyzing each frame of gestures separately. For accurate dynamic gesture recognition, motion feature extraction algorithms need to find representative features that uniquely identify time-varying gestures. This paper proposes a new feature-extraction algorithm using temporal self-similarity based on a hierarchical human model. Because a conventional temporal self-similarity method computes a whole movement among the continuous frames, the conventional temporal self-similarity method cannot recognize different gestures with the same amount of movement. The proposed model-based temporal self-similarity method groups body parts of a hierarchical model into several sets and calculates movements for each set. While recognition results can depend on how the sets are made, the best way to find optimal sets is to separate frequently used body parts from less-used body parts. Then, we apply a multiclass support vector machine whose optimization algorithm is based on structural support vector machines. In this paper, the effectiveness of the proposed feature extraction algorithm is demonstrated in an application for taebo gesture recognition. We show that the model-based temporal self-similarity method can overcome the shortcomings of the conventional temporal self-similarity method and the recognition results of the model-based method are superior to that of the conventional method.

• Journal of Intelligence and Information Systems
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• v.9 no.1
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• pp.179-193
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• 2003

Clustering is a data mining method which help discovering interesting data groups in large databases. In traditional data clustering, similarity between objects in the cluster is measured by pairwise similarity of objects. But we devise an advanced measurement called item similarity in this paper, in terms of nature of clustering transaction data and use this measurement to perform clustering. This new algorithm show the similarity by accepting the concept of relationship between different attributes. With this item similarity measurement, we develop an efficient clustering algorithm for target marketing in each group.